VES Mathematics PLCSession 2: We’ve Got Problems11/13/12

Speaking of Problems. . .

How do we know a good problem?

A Good Problem... Involves a question that cannot be

immediately answered Is challenging to the learner Holds the learner’s interest Might have more than one answer Might have only one answer, but many

different approaches to the solution Is often connected to real life

If it can be solved using a procedure or algorithm it is

not a “problem” it is an exercise.

What is a problem at one time to one person may be

an exercise to another.

Student Behaviors

The Problem

Teacher Behaviors

Problem Solving

Classroom Environment Risk taking Provide enough time Respect for each other’s thinking Opportunity to discuss and challenge

solutions Values perseverance

The Role of the Teacher is crucial...

in choosing the problem in determining how to present the

problem in determining how students will work in order to assess what the students

have learned for facilitating student communication

Where do you find problems?

Intermediate Problem

The John Hancock Building in Chicago is 1,127 feet tall. Another skyscraper in Chicago, the Amoco Building, is 1,136 feet tall. Which building is taller?

Primary Problem

There are 18 students in Mrs. Smith’s class. She wants to put them into pairs. How many pairs are there?

What challenges did you face as you rewrote the problem?

There is no other decision that teachers make that has a greater impact on

students’ opportunity to learn and on their perceptions about what mathematics is

than the selection of the tasks (or problems) with which the teacher engages

the students in studying mathematics.Lappan and Briars, 1995

There are 25 sheep and 5 dogs in a flock. How old is the Shepherd?

How many rectangles are there on a standard 8 X 8 checkerboard? Count only those rectangles (including squares) whose sides lie on grid lines. For example, there are nine rectangles on a 2 X 2 board.

1 2

3 4

5

697 8

Problem Solving: Sample

Problem Solving: Sample

The Value of this problem• Deciding what determines a rectangle• Examining a simpler problem• Adding sequence of consecutive integers• Problem lends itself to discovering mathematical

applications based on number concepts• Multiple correct solution strategies can be

applied to arrive at a solution• Variety of solutions

There are 9 cows in the barn. How many eyes are there?

Sergi’s basketball team is traveling for a tournament. There are 13 kids on the team. If each car holds 3 kids, how many cars are needed for the team to get to the tournament?